求解定态中子输运方程的非相容DSA方法  

An Inconsistent Diffusion Synthetic Acceleration Method for Stationary Neutron Transport Equations

作　　者：吴梦梦 袁达明 郑华盛[2] WU Meng-meng;YUAN Da-ming;Zheng Hua-sheng(College of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330000,China;College of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330000 [2]南昌航空大学数学与信息科学学院,江西南昌330063

出　　处：《数学的实践与认识》2020年第15期195-201,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金地区项目(11261040,11861039);江西省教育厅科技项目(高散射中子输运方程DSA方法的研究);江西省自然科学基金(2014M560918)。

摘　　要：在数值方法求解低泄漏或低俘获的粒子输运方程时,常用的源迭代法(Source iteration method,SI)收敛较慢.缓慢的迭代过程不仅效率低,并且难以确定迭代何时收敛.在已有众多的迭代加速方案中,扩散综合加速法(diffusion synthetic acceleration method,DSA)是一种有效且鲁棒的加速方法.对于一致离散DSA方法,高阶输运方程和低阶扩散算子应该满足相容性条件.然而,在处理复杂离散系统时,却很难推导出满足一致相容性条件的方法.提出了一个满足部分相容性条件的方法,即带阻尼的DSA方法.利用间断有限元方法(diffusion Galerkin method,DGA)对中子输运方程空间坐标进行离散,并利用傅里叶分析结果选择阻尼因子β.方法可用于求解定义在一维平面几何中的输运方程.傅里叶分析和数值试验表明了方法的有效性.For particle transport equation with low probability of leakage or capture,the standard source iteration method will convergent slowly.Unfortunately,the slowly converging is inefficient and it can be difficult to determine when their iterations are suitably converged.Many practical iteration acceleration schemes were developed.Among them,the Diffusion Synthetic Acceleration(DSA)can speed a discretized source iteration scheme in an efficient and robust manner.For consistently discretized DSA equations,however,the high-order transport and low-order diffusion operators should be discretized consistently.When the modeled system is complicated,it is difficult to derive the consistent schemes.In this paper,we develop an inconsistent DSA scheme for solving the steady-state transport equation define in the planar geometry in one dimension.Fourier analysis and numerical tests are showed to testify the efficiency of the proposed method.

关 键 词：输运方程 SI方法 DG方法 傅里叶分析 带阻尼DSA方法 

分 类 号：O241.6[理学—计算数学]